When I used to chamber in the steady...
Breech end in 4-jaw, dialed in barrel OD. Muzzle end in live center, make a truing cut for about an inch at the end to get OD concentric with the bore. Truing cut is pretty deep- enough to make a decent shoulder.
Flip end over end, muzzle in a collet or set-tru.
You'd need a truing cut on the muzzle long enough to get your indicator on it outside the chuck jaws, but then you'd be able to dial it in. The downside to doing it with the 4-jaw and not a set-tru or collet- is that you won't have a shoulder to seat against the chuck jaws or collet face. This prevents cutting forces from pressing the barrel further into the jaws which will ruin your day.
Dead center in the headstock is fine- but requires the additional step of securing the dog to the faceplate, which I always found to be a big PITA. Once the steady is set, and the tailstock is removed there's nothing to stop the barrel from sliding forward if you don't.